Business Statistics MBA Questions and Answers

Which of the following is an assumption of one-way anova comparing sample from three or exprimental treatments?

Ans-all of the above

____test would be best weather the population means is less than a specified value

Ans- one tail hypothesis

A statement about a population for testing purpose is called___

Ans- hypothesis

___ Is just another team for variance that is used in the analysis of variance

Ans- mean square

In a simple linear regression to determine whether the slope is statistically significant which test do we use an alternative of t test

Ans- f-test/ none of these

What should be data is assumption for one way anova z-test

Ans- homogeneity of variance/ all of these

Analysis of variance is a statistical method of comparing the ___ of several population

Ans- means

It is known that the variance of a population equal …. A random sample of 121 has been taken from the population there is a 95 probability that the mean will provide a margin of error of

Ans- 7.84 or Less

Name the technique used to make comparisons between all pairs of group

Ans- Chisquare

Consider a set of 18 samples from a standard normal distribution we square each sample and sum all the squares the number of degrees of freedom square distribution will be

Ans- 18

Whenever the population standard deviation is unknown and the population has a normal or near-normal distribution which distribution is used in developing the interval estimation

Ans- t distribution

ANOM stands for

Ans- analysis of mean

Which of the following distribution is continuous

Ans- F- Distribution

If a null hypothesis is rejected at the 0.025 level significance

Ans- may or may not be rejected at the 0.1 level

For a two tailed test, sample of 20 at 80% confidence t=

Ans- 1.328

Using an a=0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75 if the level of significance is decreased the interval population proposition

Ans- becomes wider

A sample of 20 items from a population return unknown s is selected in order to develop an interval estimate of m which of the following is necessary

Ans- the sample must have a normal distribution

some important assumption must be satisfied by a t test when assumption are related

Ans- all of these

__ is used to measure autocorrelation

Durbin Watson statistic

interval estimation of m or sample size is large

normal distribution

chi square test is extended to compare more than two ___

independent

On which of the following does the critical value for a chi-square static rely.

The degree of freedom

Which parametric test can be used to find the difference in perception about Metro services

We can evaluate the assumption of ———— of the errors by plotting the residuals.

Normality.

in order to estimate average time spend on the computer terminal per student

0.26

8.74 to 9.26 hours

In a simple linear regression to determine whether the slope is statistically significant which test do we use as an alternative of t test.

- none of these

Find Variance for an F-Distribution with v1=5 and v2=9.

1.587

In a two-tail test for the population mean, if the null hypothesis is reject

a correct decision is made

In ________ problem solving approach, you define the business objective as

A Cumulative relative frequency distribution shows

the proportion of data items with values less than or equal to the upper limit of each class.

An alternative to critical value approach is

Z value

what is b0 in regression analysis?

The value of the outcome when the predictor variable is zero.

in Hypothesis testing if the null hypothesis has been rejected when the alternative is true

A correct decision is made

A type 1 error occurs when we ————–

reject a true null hypothesis

A two-tailed test is performed at 95% confidence. The p-valueis determined to be 0.09. the null

should not be rejected

if you assume that the difference scores are randomly and independently selected

on which of the following does the critical value for a chi-square statistic rely

The degrees of Freedom

We can evaluate the assumption of ——– of the errors by plotting the residuals in the order.

Normality

Some important assumptions must be satisfied by a t-test, which assumptionare related to the samples collected for testing.

All of these

In determining the sample size necessary to estimate a population proportion ,

the mean of the population

The difference between the lower class limits of adjacent classes provided the

class width

For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t =

1.74

______ is another term for variance that is used in the analysis of variance.

Mean square

Parametric statistical test examples are :

T-test

name a non-parametric procedure when only the homogeneity-of-variance

Kruskai-wallis rank test

An interval estimate is a range of values used to estimate

a population parameter

Which of the following is a robust test?

t-test

______ is to express the desired sample as the statistical sum

Inverse method

Which of the following value of chi-square distribution cannot occur?

-2.45

if you assume that difference scores are randomly and independently selected from a

which test will you use if you have a numerical variable and related samples?

paired t-test

The degrees of freedom for the F-test in a one-way ANOVA are

(c-1) and (n – c )

Children can learn a second language faster before the age of 7. This statement is_____

A one-tailed hypothesis

A statement made about a population for testing purpose is called____

Hypothesis

The following test can be used to determine the type of distribution of any data set.

One sample K-S test

For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t =

1.316

Poisson distribution is applied for _________

Discrete random variable

for a two tailed test at 86.12% confidence, Z =

1.48

Sum of square errors (SSE) represents:

continous variation

In testing a hypothesis using the chi-square test, the theoretical frequencies are based on the

Null Hypothesis

We can evaluate the assumption of ———- in the error by constructing a histogram.

Normality

In syntax of linear model Im (formula, data,…) data refers to______

Vector

What assumptions is being made when we use the t-distribution to perform a hypothesis test?

That the underlying population follows an approximately Normal distribution

F distribution properties fall into which of the following?

A.

The mean of the f- distribution is equal to________

v2 / ( v2-2) for v2>2

In a scatter diagram, a line that provides an approx. of the relationship between

trend line

What would be then consequences for the OLS estimator if heteroscedasticity is present

it will be inefficient

If a null hypothesis is rejected at the gency level of significance

may or may not be rejected at the 0.1 level

Hypothesis test concerning a single parameter is;

All of these

A Tabular method that can be used to summarize the data on two variables simultaneously is called

crosstabulation

an estimate of a population parameter that providesin interval of values believed to contain the value of the parameters

Interval estimate

Chi-square is used to analyse:

Frequencies

Data that provide labels or names for categories of like items are known as

Qualitative

whenever using the t distribution in estimation, we must assure that

the population is approximately normal

independent simple random samples are taken to test the difference between

t distribution with 58 degrees of freedom

which of the following statistical tests allows causal inferences to be made?

none of these

For a one-tailed test (upper tail), a sample size of 22 at 95% confidence, t =

-1.717

A 95% confidence interval for a population mean is determined to be 100 to 120.

becomes narrower

which test will you use if you have a numerical variable and

paired t-test

Two-way contingency table displays the following

Comparing the courts of categorical responses between (C)

The p–value

is a probability

LIN are

Linearity

if we change a 95% confidence interval estimate to a 99% confidence

the size of the confidence interval to increase

for a two-tailed at 98.4% confidence, Z =

2.41

Which of the following is not an assumption for simple linear regression?

Multicollinearity

All financial brokers use some version of which Monte Carlo-based

data driven Black box simulator

If a hypothesis is rejected at 95% confidence, if

will always be rejected at 90% confidence

As the sample size increases, the sampling error

decreases

Which of the following distributions is continuous?

F – Distribution

We can evaluate the assumption of ______ in the error by constructing a histogram.

Plotting the residual in the order or sequence.

for a one – tailed test (lower tail) at 93.7% confidence, Z=

-1.53

What is the meaning of the term heteroscedasticity.

The Variance of the errors is not constant

_______ test would test whether the population mean is less than a specific value.

both of these

IF in a linear regression model the train error is zero, then

Couldn’t comment on test error

Find the expectation for a F-distribution variable with v1 = 7 and v2 = 8

4/3

F- test is used if certain conditions are met like

Variance of the two populations are known

What proportion of lamps will fail before 925 hours?

0.16

.78. How many lamps will fail before 900 hrs.

A.4560

How many lamps will fail between 950 and 1000 hrs.

1250

Given the same mean life, what would the standard deviation

100

Which of these are types of simulation models.

both of these

In developing an interval estimate, if the population standard deviation

the sample standard deviation can be used

What should be data anova for one way ANOVA z-test ?

Homogeneity of Variance

As the sample size increases, the sampling error

decreases

if you assume that the difference scores are randomly and independently selected

None of these

when a histogram has a longer tail to the right, it is said to be

skewed to the right

If my null hypothesis is ‘ Dutch people do not differ from English

All of the statement below are plausible alternate hypothesis

In hypothesis testing if the null hypothesis is rejected

the alternative hypothesis is true

In a two-tailed hypothesis test the test statistic is determined to be -2.5. the p-value for this tets

0.0124

A probability statement about the sampling error is known as the

Precision

A frequency distribution is

a tabular summary of a set of data showing the frequency of items in each of several

a pooled variance t test to used to determine whether there is a significant difference between means

in anova with 4 groups and a total sample size of 44 Greater than 0.05

in a sample of 500 voters, 400 indicated they favour the incumbent governor.The 95% confidence interval of voters not favouring the incumbent is 0.165 to 0.235

- A problem-solving approach, you define te business objective as determining whether there is a difference in the mean

- Arlingtons scenario
**Dcova**- Pool variance T test
- None of these

- For a one-tailed test ( lower tail) at 89.8% confidence , Z=

**-1.27**- -1.53
- -1.96
- -1.64

- The confidence associated with an interval estimated is called the

- Significance
- Degree of association

**Confidence level**

- Precision

- Following is a two way , between – subjects anova a simple effect would involve

- Conduction one contrast
- Conducting a one way within-subjects anova
- Ignoring the existence of one IV and comparing the levels of other IV
**Taking only one level of one IV at a time and comparing the levels of other IV**

- We can evaluate the assumptions of ___ of the error by piloting the residual(52)

**Independence**- Normality
- Equal Variance
- None of these

- Which of the following is an assumption of one way anova comparing the samples from three(56)

- the sample associated with each population
- the response variable within each of the K Population
- all the response variables within the
**All of above**

- If a hypothesis test leads to rejection of the null hypothesis(60)

- A type II error must have been committed
- A type II error may have been committed
- A type I error must have been committed
**A type I error may have been committed**

- In order to use the normal distribution for interval estimation of m when s is known, the population(59)

**Must be very large**- Must have a normal distribution
- Can have any distribution
- None of the above

- In a one tailed hypothesis test ( Lower tail ) the test statistic is determined to be -2. The P value for the test is(64)

- 4772
**0228**- 0056
- 0228

- We are interested in conducting a study in order to determine what percentage of voters of a state(62)

- 200
- 100
**58**- 196

- Chi square test statistic is equal to the square difference between the ___ and ___ frequency(65)

- Observed
- Expected
**Both of these**- None of these

- a situation in which conclusion is based upon aggregate cross tabulation the different from un-aggregated cross tabulation is

- Wrong cross tabulation
- Simpson Rule
**Simpson paradox**- Aggregated cross tabulation

- In constructing a frequency distribution the approximately class width is computed as

**(Largest data value-smallest data value)/ no of class**- (Largest data value-smallest data value)/ sample size
- (smallest data value-Largest data valve/ sample size
- Largest data value X no, of classes

- Which of these are types of situation models

- Continuous models
- Discrete models
**Both of these**- None of these

- When a data value in one sample is matched with a corresponding data value in another sample.

the sample are known is

- Corresponding samples
**Matched samples**- Independent samples
- None of these alternative is correct

- In constructing a frequency distribution as the no of class are decreased. The class width

- Decreased
- Remain unchanged
**Increased**- Can increase or decrease depending upon the data value

- Independence simples random samples are taken to test the difference between the means of two population those standard deviation are not known. The sample size are n1=25 and n2=35. The correct distribution to use is the

- Poisson distribution
- T distribution with 60 degree of freedom
- T distribution with 59 degree of freedom
**T distribution with 58 degree of freedom**

- A frequency distribution is

- Tabular summary of a set of data showing the relative frequency
- A graphical form of representing data
**A tabular summary of a set of data showing the frequency of item in each of several non overlapping classes**- A graphical device for presenting qualitative data

- When the level of confidence increase, the confidence interval

- Stays the same
**Become wider**- Become narrower
- Cannot tell from the information given

- In General , Higher confidence level provide

**Wider confidence interval**- Narrower confidence interval
- Smaller standard error
- Unbiased estimate

- Suppose that we reject a null hypothesis at the 5% level of significance. For which of the following level of significance do we also reject the null hypothesis

- 0.025
**0.06**- 0.02
- 0.04

If a Hypothesis is rejected at the 5% level of significance, it

may be rejected or not rejected at the 1% level

The p-Value

is a probability

The Null Hypothesis uses ——— and the alternative hypothesis never uses an

equal sign

After computing a confidence interval, the user believes the results are meaningless because the width

Increase the sample size

Independence means ——— between the variables under study

No relationship

The Chi-square test is extended to compare more than two ___________ population.

independent

The sum of relative frequencies for all classes will always equal

one

For which regression assumptions does Durbin – Watson

Independence of errors

In a one –way ANOVA

an interaction effect can be tested

IF the Null hypothesis is false

Alternative Hypothesis

We can evaluate the assumption of ——— in the error by constructing a histogram.

Independence

The level of Significance

is (1 – confidence level)

Which of the following best describes the form of sampling distribution of the sample proportion?

It is approximately normal as long as np>= 5 and n(1-p) >= 5.

Fifteen present of the students in a school of business administration are majoring in Economics, 20% in finance, 35% in management, & 30% in accounts.

Both a bar graph and a pie chart

**REGRESSION ANALYSIS** techniques help uncover relationship between variables

for a one-tailed test upper tail a sample size of 18 at 95% confidence,t=1.740

a pooled variance t test to used to determine whether there is asignificant difference between means

inanova with 4 groups and a total sample size of 44Greater than 0.05

parametric statistical test examplesT test

In testing a hypothesis using the chi-square test, the theoretical frequencies are based on the:

A. null hypothesis

Children can learn a second language faster before the age of 7’. Is this statement:A one-tailed hypothesis

**one tail hypothesis test**would test whether the population is less than specific value

in a sample of 500 voters, 400 indicated they favour the incumbent governor.The 95% confidence interval of voters not favouring the incumbent is 0.165 to 0.235

- Which of the following is a discrete quantitative (numerical) variable?

- The Dow Jones Industrial average
- The volume of water released from a dam
- The distance you drove yesterday
- The number of employees of an insurance company <<

- Which of the following is a continuous quantitative (numerical) variable?

- The color of a student’s eyes
- The number of employees of an insurance company
- The amount of milk in a 2-liter carton <<
- The number of gallons of milk sold at the local grocery store yesterday

- To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period of time, then X is an example of a.

- categorical variable
- discrete variable <<
- continuous variable
- statistic

- Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children’s clothing should be manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study, then X is an example of

- categorical variable
- discrete variable
- continuous variable <<
- a table of random numbers

The classification of student class designation (freshman, sophomore, junior, senior) is an example of

- a categorical variable <<
- a discrete variable
- a continuous variable
- a table of random numbers

- The classification of student major (accounting, economics, management, marketing, other) is an example of

- a categorical variable <<
- a discrete variable
- a continuous variable
- va table of random numbers

- The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The answer on “whether you visited campus bars on the weekend before the final exam week” from students in the sample is an example of ___________

- a categorical variable <<
- a discrete variable
- a continuous variable
- a table of random numbers

- Referring to Scenario 1-1, the possible responses to the question “How many Blu-ray players made by other manufacturers have you used?” are values from

a a. discrete variable <<

- continuous variable
- categorical variable
- table of random numbers

- Referring to Scenario 1-1, the possible responses to the question “Are you happy, indifferent, or unhappy with the performance per dollar spent on the Blu-ray player?” are values from

a a. discrete numerical variable

- continuous numerical variable
- c. categorical variable <<
- table of random numbers

- Referring to Scenario 1-1, the possible responses to the question “What is your annual income rounded to the nearest thousands?” are values from

a a. discrete numerical variable <<

- continuous numerical variable
- categorical variable
- table of random numbers

- A type of vertical bar chart in which the categories are plotted in the descending rank order of the magnitude of their frequencies is called

a a. contingency table

- Pareto chart <<
- stem-and-leaf display
- pie chart

- The width of each bar in a histogram corresponds to the

- differences between the boundaries of the class <<
- number of observations in each class
- midpoint of each class
- percentage of observations in each class

- When constructing charts, the following is plotted at the class midpoints:

- frequency histograms
- percentage polygons <<
- cumulative percentage polygon (ogives)
- All of the above

- Which of the following is appropriate for displaying data collected on the different brands of cars students at a major university drive?

- A Pareto chart <<
- A two-way classification table
- A histogram
- A scatter plot

- One of the developing countries is experiencing a baby boom, with the number of births rising for the fifth year in a row, according to a BBC News report. Which of the following is best for displaying this data?

- A Pareto chart
- A two-way classification table
- A histogram
- A time-series plot <<

- When studying the simultaneous responses to two categorical questions, you should set up a

- contingency table <<
- frequency distribution table
- cumulative percentage distribution tabled
- histogram

- Data on 1,500 students’ height were collected at a larger university in the East Coast. Which of the following is the best chart for presenting the information?

- A pie chart
- A Pareto chart
- A side-by-side bar chart
- A histogram <<

- Data on the number of part-time hours students at a public university worked in a week were collected. Which of the following is the best chart for presenting the information?

- A pie chart
- A Pareto chart
- A percentage table
- A percentage polygon <<

- Data on the number of credit hours of 20,000 students at a public university enrolled in a Spring semester were collected. Which of the following is the best for presenting the information?

- A pie chart
- A Pareto chart
- A stem-and-leaf display <<
- A contingency table

- A survey of 150 executives were asked what they think is the most common mistake candidates make during job interviews. Six different mistakes were given. Which of the following is the best for presenting the information?

- A bar chart <<
- A histogram
- A stem-and-leaf display
- A contingency table

11.Technique help uncover relationship between variable

- I) Regression analysis <<
- II) ANOVA
- III) Hypothesis
- IV) None of these

- Which of the following statistics is not a measure of central tendency?
- Arithmetic mean b. Median
- Mode d.
**Q3**

- Which measure of central tendency can be used for both numerical and categorical variables?
- Arithmetic mean b. Median
**Mode**d. Geometric mean

- Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency?
- The arithmetic mean and median only
**The median and mode only**- The mode and geometric mean only
- The arithmetic mean and mode only

- In a right-skewed distribution
- the median equals the arithmetic mean
**the median is less than the arithmetic mean**- the median is greater than the arithmetic mean
- none of the above

- Which of the following statements about the median is not true?
**It is more affected by extreme values than the arithmetic mean**- It is a measure of central tendency
- It is equal to Q2
- It is equal to the mode in bell-shaped “normal” distributions

- In a perfectly symmetrical bell-shaped “normal” distribution
- the arithmetic mean equals the median
- the median equals the mode
- the arithmetic mean equals the mode
**All the above**

- In a perfectly symmetrical distribution
- the range equals the interquartile range
- the interquartile range equals the arithmetic mean
**the median equals the arithmetic mean**- the variance equals the estird deviation

- When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate
- CV and range
- arithmetic mean and standard deviation
**interquartile range and median**- variance and interquartile range

- In general, which of the following descriptive summary measures cannot be easily approximated from a boxplot?
**The variance b. The range**- The interquartile range d. The median

- The smaller the spread of scores around the arithmetic mean
- the smaller the interquartile range
- the smaller the standard deviation
- the smaller the coefficient of variation
**All the above**

- If two events are collectively exhaustive, what is the probability that one or the other occurs?
- 0 b. 0.50
**1.00**d. Cannot be determined from the information given

- If two events are collectively exhaustive, what is the probability that both occur at the same time?
- 0 b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two events are mutually exclusive, what is the probability that one or the other occurs?
- 0 b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two events are mutually exclusive, what is the probability that both occur at the same time?
**0**b. 0.50- 1.00 d. Cannot be determined from the information given

- If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?
**0**b. 0.50- 1.00 d. Cannot be determined from the information given

- If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?
- 0 b. 0.50
**1.00**d. Cannot be determined from the information given

- If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
- 0 .b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event

A occurs?

- 0
**b. 0.50** - 1.00 d. Cannot be determined from the information given

- If two equally likely events A and B are mutually exclusive, what is the probability that event A occurs?
- 0 b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs?
- 0 b. 0.50
- 1.00 d
**. Cannot be determined from the information given**

- Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio- Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
- 5 days b. 45 days
- 65 days
**d. 81 days**

- A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
- 0.0256
**b. 0.0625** - 0.16 d. 1.00

- A probability distribution is an equation that
**associates a particular probability of occurrence with each outcome**- measures outcomes and assigns values of X to the simple events
- assigns a value to the variability of the set of events
- assigns a value to the center of the set of events

- The connotation “expected value” or “expected gain” from playing roulette at a casino means
- the amount you expect to “gain” on a single play
**the amount you expect to “gain” in the long run over many plays**- the amount you need to “break even” over many plays
- the amount you should expect to gain if you are lucky

- A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value
- Most of the weeks resulted in rat costs of $13.00
- The median cost for the distribution of rat costs is $13.00
**The expected or mean cost for all weekly rat purchases is $13.00**- The rat cost that occurs more often than any other is $13.00

**True**or False: Another name for the mean of a probability distribution is its expected value

True

- Which of the following about the binomial distribution is not a true statement?
- The probability of the event of interest must be constant from trial to trial
- Each outcome is independent of the other
- Each outcome may be classified as either “event of interest” or “not event of interest”
**The variable of interest is continuous**

- In a binomial distribution
- the variable X is continuous
**the probability of event of interest is stable from trial to trial**- the number of trials n must be at least 30
- the results of one trial are dependent on the results of the other trials

- Whenever π = 0.5, the binomial distribution will
**always be symmetric**- be symmetric only if n is large
- be right-skewed
- be left-skewed

- Whenever π = 0.1 and n is small, the binomial distribution will be
- symmetric
**right-skewed**- left-skewed
- None of the above

- In its standardized form, the normal distribution
**has a mean of 0 and a standard deviation of 1.**- has a mean of 1 and a variance of 0.
- has an area equal to 0.5.
- cannot be used to approximate discrete probability distributions.

- Which of the following about the normal distribution is not true?
- Theoretically, the mean, median, and mode are the same.
- About 2/3 of the observations fall within } 1 standard deviation from the mean.
**It is a discrete probability distribution.**- Its parameters are the mean,
*μ*, and standard deviation, σ.

- If a particular set of data is approximately normally distributed, we would find that approximately
- 2 of every 3 observations would fall between } 1 standard deviation around the mean.
- 4 of every 5 observations would fall between } 1.28 standard deviations around the mean.
- 19 of every 20 observations would fall between } 2 standard deviations around the mean.
**All the above.**

- The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is:
- 0.18 b. 0.81
**1.16**d. 1.47

- For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is:
**– 0.81**b. – 0.31- 0.31 d. 1.96

- For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. The value of Z is:
- 0.07 b. 0.37
**0.97**d. 1.06

- The value of the cumulative standardized normal distribution at Z is 0.6255. The value of Z is:
- 0.99 b. 0.40
- c
**. 0.32**0.16

- The value of the cumulative standardized normal distribution at 1.5X is 0.9332. The value of X is:
- 0.10 b. 0.50
**1.00**d. 1.50

- If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
- 0.3551
**b. 0.3085** - 0.2674 d. 0.1915

- If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.
- 0.0919 b. 0.2255
- 0.4938
**d. 0.7745**

- In its standardized form, the normal distribution
**has a mean of 0 and a standard deviation of 1.**- has a mean of 1 and a variance of 0.
- has an area equal to 0.5.
- cannot be used to approximate discrete probability distributions.

- Which of the following about the normal distribution is not true?
- Theoretically, the mean, median, and mode are the same.
- About 2/3 of the observations fall within } 1 standard deviation from the mean.
**It is a discrete probability distribution.**- Its parameters are the mean,
*μ*, and standard deviation, σ.

- If a particular set of data is approximately normally distributed, we would find that approximately
- 2 of every 3 observations would fall between } 1 standard deviation around the mean.
- 4 of every 5 observations would fall between } 1.28 standard deviations around the mean.
- 19 of every 20 observations would fall between } 2 standard deviations around the mean.
**All the above.**

- The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is:
- 0.18 b. 0.81
**1.16**d. 1.47

- For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is:
**– 0.81**b. – 0.31- 0.31 d. 1.96

- For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. The value of Z is:
- 0.07 b. 0.37
**0.97**d. 1.06

- The value of the cumulative standardized normal distribution at Z is 0.6255. The value of Z is:
- 0.99 b. 0.40
**0.32**d. 0.16

- The value of the cumulative standardized normal distribution at 1.5X is 0.9332. The value of X is:
- 0.10 b. 0.50
**1.00**d. 1.50

- If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.
- 0.3551
**b. 0.3085** - 0.2674 d. 0.1915

- If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.
- 0.0919 b. 0.2255
- 0.4938
**d. 0.7745**

- Sampling distributions describe the distribution of
- parameters b
**. statistics** - both parameters and statistics d. neither parameters nor statistics

- The standard error of the mean
- is never larger than the standard deviation of the population
- decreases as the sample size increases
- measures the variability of the mean from sample to sample
**All of the above**

- The Central Limit Theorem is important in statistics because
- for a large n, it says the population is approximately normal
- for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the samplesize
**for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population**- for any sized sample, it says the sampling distribution of the sample mean is approximately normal

- If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic
**unbiased**b. minimum variance- biased d. random

- For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.
- Distribution is right skewed with mean = 10 minutes and standard error = 0.8 minutes
- Distribution is right skewed with mean = 10 minutes and standard error = 8 minutes
**Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes**- Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes

- Which of the following statements about the sampling distribution of the sample mean is

incorrect?

- The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (
*n*>30). - The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.
- The mean of the sampling distribution of the sample mean is equal to.
**The standard deviation of the sampling distribution of the sample mean is equal to.**

- Which of the following is true about the sampling distribution of the sample mean?
**The mean of the sampling distribution is always.**- The standard deviation of the sampling distribution is always.
- The shape of the sampling distribution is always approximately normal.
- All of the above are true.

- True or False: The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

**True**

- Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?
- The mean of the sampling distribution is equal to 23 years.
**The standard deviation of the sampling distribution is equal to 3 years.**- The shape of the sampling distribution is approximately normal.
- The standard error of the sampling distribution is equal to 0.3 years.

- Why is the Central Limit Theorem so important to the study of sampling distributions?
- It allows us to disregard the size of the sample selected when the population is not normal.
- It allows us to disregard the shape of the sampling distribution when the size of the population is large.
- It allows us to disregard the size of the population we are sampling from.
**d. It allows us to disregard the shape of the population when n is large.**

1.Which of the following would be an appropriate null hypothesis?

**The mean of a population is equal to 55**- The mean of a sample is equal to 55
- The mean of a population is greater than 55
- Only (a. and (c. are appropriate

- Which of the following would be an appropriate null hypothesis?
- The population proportion is less than 0.65
- The sample proportion is less than 0.65
**The population proportion is not less than 0.65**- The sample proportion is no less than 0.65

- Which of the following would be an appropriate alternative hypothesis?
- The mean of a population is equal to 55
- The mean of a sample is equal to 55
**The mean of a population is greater than 55**- The mean of a sample is greater than 55

- Which of the following would be an appropriate alternative hypothesis?
**The population proportion is less than 0.65**- The sample proportion is less than 0.65
- The population proportion is not less than 0.65
- The sample proportion is not less than 0.65

- A Type II error is committed when
- you reject a null hypothesis that is true
- you don’t reject a null hypothesis that is true
- you reject a null hypothesis that is false
**you don’t reject a null hypothesis that is false**

- A Type I error is committed when
**you reject a null hypothesis that is true**- you don’t reject a null hypothesis that is true
- you reject a null hypothesis that is false
- you don’t reject a null hypothesis that is false

- The power of a test is measured by its capability of
- rejecting a null hypothesis that is true
- not rejecting a null hypothesis that is true
**rejecting a null hypothesis that is false**- not rejecting a null hypothesis that is false

- If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000
- either a one-tail or two-tail test could be used with equivalent results
**a one-tail test should be utilized**- a two-tail test should be utilized
- None of the above

- If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000
- either a one-tail or two-tail test could be used with equivalent results
- a one-tail test should be utilized
**a two-tail test should be utilized**- None of the above

- If the p-value is less than in a two-tail test,
- the null hypothesis should not be rejected
**the null hypothesis should be rejected**- a one-tail test should be used
- no conclusion should be reached

**True or**False**:**For all two-sample tests, the sample sizes must be equal in the two groups.

- True
**or False:**When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

- The t test for the difference between the means of 2 independent populations assumes that the respective
- sample sizes are equal
- sample variances are equal
**populations are approximately normal**- All of the above

- If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of
*n*1 = 20 and*n*2 = 20, the number of degrees of freedom is equal to - 39 b.
- If two events are collectively exhaustive, what is the probability that one or the other occurs?
- 0 b. 0.50
**1.00**d. Cannot be determined from the information given

- If two events are collectively exhaustive, what is the probability that both occur at the same time?
- 0 b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two events are mutually exclusive, what is the probability that one or the other occurs?
- 0 b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two events are mutually exclusive, what is the probability that both occur at the same time?
**0**b. 0.50- 1.00 d. Cannot be determined from the information given

- If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?
**0**b. 0.50- 1.00 d. Cannot be determined from the information given

- If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?
- 0 b. 0.50
**1.00**d. Cannot be determined from the information given

- If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
- 0 .b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event

A occurs?

- 0
**b. 0.50** - 1.00 d. Cannot be determined from the information given

- If two equally likely events A and B are mutually exclusive, what is the probability that event A occurs?
- 0 b. 0.50
- 1.00
**d. Cannot be determined from the information given**

- If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs?
- 0 b. 0.50
- 1.00 d
**. Cannot be determined from the information given**

- Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio- Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
- 5 days b. 45 days
- 65 days
**d. 81 days**

- In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are
*n*– 1*n*1 +*n*2 – 1*n***1 + n2 – 2***n*– 2

- Given the following information, calculate
*s*p2, the pooled sample variance that should be used in the pooled-variance*t*test.

*s*12 = 4 *s*22 = 6

*n*1 = 16 *n*2 = 25

*sp*2 = 6.00*sp*2 = 5.00*sp***2 = 5.23***sp*2 = 4.00

* *

- True
**or False:**The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

- True
**or False:**When you test for differences between the means of two independent populations, you can only use a two tail test.

- True
**or False:**A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.

**True or**False**:**A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.

- In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may
- reject H0 since there is evidence all the means differ
**reject H0 since there is evidence that not all the means are different**- not reject H0 since there is no evidence of a difference in the means
- not reject H0 because a mistake has been made

- Which of the following components in an ANOVA table are not additive?
- Sum of squares
- Degrees of freedom
**Mean squares**- It is not possible to tell

- When would you use the Tukey-Kramer procedure?
- To test for normality
- To test for homogeneity of variance
- To test independence of errors
**To test for differences in pairs of means**

- A completely randomized design
**has only one factor with several treatment groups**- can have more than one factor, each with several treatment groups
- has one factor and one block
- has one factor and one block and multiple values

- The F test statistic in a one-way ANOVA is
- MSW/MSA
- SSW/SSA
**MSA/MSW**- SSA/SSW

- The degrees of freedom for the F test in a one-way ANOVA are
- (
*n*–*c*) and (*c*– 1) **(***c*– 1) and (*n*–*c*)- (
*c*–*n*) and (*n*– 1) - (
*n*– 1) and (*c*–*n*)

- In a one-way ANOVA, the null hypothesis is always
**there is no difference in the population means**- there is some treatment effect
- all the population means are different
- some of the population means are different

- In a one-way ANOVA
- an interaction term is present
- an interaction effect can be tested
**there is no interaction term**- the interaction term has (
*c*– 1)(*n*– 1) degrees of freedom

- True
**or False:**The analysis of variance (ANOVA) tests hypotheses about the population variance

**True or**False**:**When the F test is used for ANOVA, the rejection region is always in the right tail

- If we use the x2 method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:
**3**b. 4- 5 d. 1

- If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group

2, the appropriate test to use is

- the Z test b. the x2 test
**Both a) and b)**d. Neither of a) nor b)

- In testing a hypothesis using the x2 test, the theoretical frequencies are based on the
**null hypothesis**- alternative hypothesis
- normal distribution
- None of the above

**True**or False: In testing the difference between two proportions using the normal distribution, we may use either a one-tail Chi-square test or two-tail*Z*test.

- True or
**False**: The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.

**True**or False: A test for the difference between two proportions can be performed using the chi- square distribution.

- True or
**False**: A test for whether one proportion is higher than the other can be performed using the chi-square distribution.

- When testing for independence in a contingency table with 3 rows and 4 columns, there are degrees of freedom.
- 5 b.
**6** - 7 d. 12

- To use the Wilcoxon Rank Sum Test as a test for location, you must assume that
- the obtained data are either ranks or numerical measurements that will be converted to combined ranks
- both samples are randomly and independently drawn from their respective populations
- both underlying populations from which the samples were drawn are equivalent in shape and dispersion
**All the above**

- Which of the following is a “robust” test procedure against the violation of distribution assumptions?
- x2 -test of independence
- McNemar test for the difference between two proportions
- x2 -test for the differences among more than two proportions
**Wilcoxon rank sum test for difference in medians**

The Y-intercept (*b*0) represents the

**predicted value of***Y*when*X*= 0- change in estimated
*Y*per unit change in*X* - predicted value of
*Y* - variation around the sample regression line

- The Y-intercept (
*b*0) represents the **estimated average***Y*when*X*= 0- change in estimated average
*Y*per unit change in*X* - predicted value of
*Y* - variation around the sample regression line
- The slope (
*b*1) represents - predicted value of
*Y*when*X*= 0 **the estimated average change in***Y*per unit change in*X*- the predicted value of
*Y* - variation around the line of regression

- The least squares method minimizes which of the following?
- SSR
**SSE**- SST
- All of the above

**True**or False: The Chancellor of a university has commissioned a team to collect data on students’ GPAs and the amount of time they spend bar hopping every week (measured in minutes). He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students’ GPAs. His team should use a t test on the slope of the population regression.

- The residual represents the discrepancy between the observed dependent variable and its__
**predicted or estimated mean**_____value.

- If the Durbin-Watson statistic has a value close to 0, which assumption is violated?
- Normality of the errors
**Independence of errors**- Homoscedasticity
- None of the above

- If the Durbin-Watson statistic has a value close to 4, which assumption is violated?
- Normality of the errors
**Independence of errors**- Homoscedasticity
- None of the above

- The standard error of the estimate is a measure of
- total variation of the
*Y*variable **the variation around the sample regression line**- explained variation
- the variation of the
*X*variable

- The coefficient of determination (
*r*2) tells you - that the coefficient of correlation (
*r*) is larger than 1 - whether r has any significance
- that you should not partition the total variation
**the proportion of total variation that is explained**

- While assigning random numbers in Monte Carlo simulation, it is?
- Necessary to assign the particular appropriate random numbers
**Necessary to develop a cumulative probability distribution**- To ensure all the points in square are equally probable
- Not necessary to assign the exact range of random number

- As simulation is not an analytical model, therefore the result of simulation must be viewed as?
- Unrealistic
- Exact
**Approximation**- Simplified

- The two types of simulation are?
**Continuous model and discrete model**- Variable and non variable model
- Average and service facility model
- Behaviour and waiting lines model

- Biased random sampling is made from among alternatives which have?
- Equal probability
**Unequal probability**- Probability which do not sum to 1
- Probability which sum to 1

- Randomness in simulation arises when the interval between successive events is?
**Probabilistic**- Invariable
- Exponential
- Convolution

- Which of the following is not a sampling from probability distributions?
- Inverse method
**Simplex method**- Convolution method
- Rejection method

- Simulation is defined as?
- Requires programme writing
- Difficult to create the appropriate events
**A procedure for testing & experimenting on models**- Adequate level of user participation

- Stimulation is a statistical experiment and it should satisfy which of the below condition?
**Observations are independent**- Requires predefined coding forms
- Sampled to be drawn
- Distributions to be observed

- Which of the below is the most common methods of collecting observations in simulation?
**Subinterval method**- Interval method
- Independent method
- Non replication method

- The important step required for simulation approach in solving a problem is to?
**Test & validate and design the model**- Appropriate level of detail
- Decision making
- Simulating

- Index numbers are used to
- Compare the phenomenon from one time period to another time period
**Identify the ratio between two time periods**- Find the average between two time periods
- None of the above

- Index number for period i =
- i = (value in period i / value in base period)
- i = (value in base period / value in period) × (value in period i / value in base period)
**i = (value in period i / value in base period) × 100**- i = (value in base period / value in period) × 100

- An index number is called a simple index when it is computed from?
**Single variable**b. Multiple variables- Bi-variable d. Non variable

- Unweighted aggregate price index numbers and weighted aggregate price index numbers are the two caterogeries of?
- Index number
**Price index number**- Laypeyre’s index number
- Paasche’s index number

- Index numbers are used for?
**Forecasting**b. Fixed price- Different price d. Constant price

- Index for base period is always taken as?
- 200 b. 10
**100**d. 1

- How many types are used for the calculation of weighted aggregate price index numbers?
- 7 b. 4
- 5 d.
**6**

- What is the formula used in Laspeyres’s Price Index Number?
**i = (Σ***p*1*q*0 / Σ*p*0*q*0) × 100- i = (Σ
*p*1*q*1 / Σ*p*0*q*1) × 100 - i = (Σ
*p*1*q*1 / Σ*p*0*q*0) × 100 - i = (Σ
*p*1*q*0 / Σ*p*1*q*1) × 100

- Which of the below index number is the arithmetic mean of Laspeyres’s price index and Paasche’s price index?
- Marshall–Edgeworth Price Index Number
**Dorbish–Bowley Price Index Number**- Bowley Price Index Number
- Walsch Price Index Number

- The most commonly used index number is?
- Simple index number
- Volume index number
**Value index number**- Price index number

- In testing a hypothesis using the chi square test, the theoretical frequencies are based on the

**Null hypothesis**- Alternate hypothesis

- Normal Distribution

- None of these

- The confidence associated with an interval estimated is called the

- Significance
- Degree of association

**Confidence level**

Precision

- Which test will you use if you have a numerical variable and related sample(55)

**Paired T test**- Z-test

- F-test

- All of these

- Which of the following is an assumption of one way anova comparing the samples from three(56)

- the sample associated with each population
- the response variable within each of the K Population

- all the response variables within the

**All of above**

- Which of the following values of the chi-sqaure distribution cannot occur?(57)

- 61
**-2.45**

- 4

- 100

- In a two tail test for the population mean , if the null hypothesis is rejected when the alternate is true

- A one tailed test should be used instead of two tail test(58)
- Type I error is committed

- A type II error is committed

**A correct decision is made**

- Test would test whether the population is less than specific value(54)

- One tailed hypothesis
- Two tail hypothesis

**Both of these**

- None of these

- If a hypothesis test leads to rejection of the null hypothesis(60)

- A type II error must have been committed
- A type II error may have been committed

- A type I error must have been committed

**A type I error may have been committed**

- In order to use the normal distribution for interval estimation of m when s is known, the population(59)

**Must be very large**- Must have a normal distribution

- Can have any distribution

- None of the above

- A tailed test is performed at 95% confidence. The P value is determined to be 0.09. the null hypothesis(61)

- Must be rejected
**Should not be rejected**- Could be rejected depending on the sample size
- Has been designed incorrectly

- What is B0 in Regression analysis(66)

**The value of the outcome when all of the predictors are zero**- The relationship between a predictor and the outcome variable
- The value of the outcome when the predictor variable is zero
- The gradient of the regression line

- We can evaluate the assumption of ___ in the errors by constructing a histogram(63)

**Normalities**- Independence
- Plotting the residuals in the order or sequence in which the data were collected
- None of these

- Chi square test statistic is equal to the square difference between the ___ and ___ frequency(65)

- Observed
- Expected
**Both of these**- None of these

- Estimate of a population parameter that provide in interval of values believed to contain the value of the parameters

- Confidence level
**Interval estimate**- Parameter value

- Population estimate

- a situation in which conclusion is based upon aggregate cross tabulation the different from un-aggregated cross tabulation is

- Wrong cross tabulation
- Simpson Rule
**Simpson paradox**- Aggregated cross tabulation

- In syntax of linear model IM ( formula, data ) data refer to ___

- Matrix
**Vector**- Array
- List

- When a histogram has a longer tail to the right. It is said to be

- Symmetrical
- Skewed to the left
**Skewed to the right**- None of these alternate is correct

- In constructing a frequency distribution the approximately class width is computed as

**(Largest data value-smallest data value)/ no of class**- (Largest data value-smallest data value)/ sample size
- (smallest data value-Largest data valve/ sample size
- Largest data value X no, of classes

- When a data value in one sample is matched with a corresponding data value in another sample. the sample are known is

- Corresponding samples
**Matched samples**- Independent samples
- None of these alternative is correct

- What is the means of the term “heteroskedasticity”

**The variance of the error is not constant**- The variance of the depended variable is not constant
- The error are not linear independent of one another
- The error as non-zero means

- In constructing a frequency distribution as the no of class are decreased. The class width

- Decreased
- Remain unchanged
**Increased**

- Can increase or decrease depending upon the data value

- A tubular method that can be used to summarize the data on two variable simultaneously is called

- Simultaneously equation
**Cross tabulation**- Histogram
- Ogive

- In order to estimate the average time spend on the computer terminals per student at a local university. Data were collected for a sample of 81 business student over a one week period. Assume the population standard deviation is 1.2 hrs. If the sample mean is 9 hours. Then the 95% confidence interval is

- 04 to 110.96 hrs
- 36 to 10.64
- 80 to 10.20
**74 to 9.26**

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